NOTE: It is hard to correctly type the piecewise-defined functions using a regular keyboard.

I hope you can understand the above.

I'll do the first one for you- graph it. The conditions are the "if" parts in the piece-wise function. Domain is (-3, inf) and there are no intersepts. Try graphing it. You have a line with slope = 1 and an exponential function.

EDIT: Sorry, there are x and y-intercepts, as Soroban pointed out, although the two graphs do not not intersect which is what I was getting at.

No, I did not sketch the graph because I do not know how to graph piecewise-defined functions.

I understand these functions are graphed in parts, right?

Can you take me through a sample graphing question in terms of this type of function?

Thanks!

Yes, they are 'graphed in parts,' I guess you could call it.

For instance,

Take the first condition;

f(x) = 3 + x if -3 <= x < 0

From x = -3 (including this point) to x = 0 (not including, and thus draw an open circle by this point), you will graph 3 + x; see Soroban's graph. The reason why it's closed (solid dot) is because of the next condition later, and thus includes that point. Try look up piece-wise functions on Wikipedia.